Poll: 6÷2(1+2)

[dowie]

The biggest problem here is once it's been explained posters ignore it and continue on their same unaltered line on the next page. Such is the interwebs.

Yes, quite.

It has already been explained that it is 9 yet people are still trying to argue incorrectly that its 'ambiguous'.

 

[gambitt]

Just look up which has priority multiply or divide

Neither one has precedence over the other but some people are applying something called the "left to right rule" which is something that primary school teachers made up out of convenience.

Either answer is acceptable.

 

[gambitt]

I've not mentioned BODMAS specifically tbh.. But you're being incredibly naive if you don't believe you follow conventions when solving equations.

Everything can be proved from first principals, so where did this "left to right convention" come from? Why does it have to be used at all? Can you find any information about it other than some primary school examples?

Let me guess "err... you're sidetracking the thread"

 

[wmb]

So there are "implied bracket" i.e, for BODMAS to work with this example you have to add brackets as you have to do the addition first (even though there;s no need to actually have them as shown).

But wait, the original point of this thread, the ambiguous phrasing of an equation, implies to a lot of people that the denominator is 2(1+2) as it is not written in standard form and are therefore suggesting it could easily be interpreted as (2(1+2)) hence the suggestion the answer could be 1 as much as it could be 9.

Please explain to us, how you can state that by implication it is fine for you to add brackets to my example (just so BODMAS works), yet it is not OK for people to add brackets into the original equation.

 

[dowie]

Everything can be proved from first principals, so where did this "left to right convention" come from? Why does it have to be used at all? Can you find any information about it other than some primary school examples?

Let me guess "err... you're sidetracking the thread"

Explain why 2x^2 is read as 2(x^2) rather than (2x)^2 other than simply by convention.

 

[silversurfer]

yes left to right rule is bs. There is an order of operations, certain parts of the equation are done first and independently of what surrounds it like obviously within the brackets.

I may have completely forgotten what that order is but its not as simple left to right unfortunately

Either answer is acceptable.

Got to disagree there though. Think of engineering and that kind of thing, two answers is not an acceptable situation for the calculation of a dimension, etc

There is a set order and only one answer, put it into a computer and it'll know . Google even

The standard order of operations, or precedence, is expressed here:
terms inside parenthesis
exponents and roots
multiplication and division
addition and subtraction

 

[guyfawkes5]

Yes, quite.

It has already been explained that it is 9 yet people are still trying to argue incorrectly that its 'ambiguous'.

Haw-haw-haw you must be a riot at conventions...

Here you go, I found it a couple of pages back; I await silence or sidetracking, your choice:

I didn't make any attempt to answer the question and I've given my view on it by my comments, in that its poor/sloppy notation. I would never write such a thing myself and if anyone else did I'd ask for clarification. Typically if you spend a lot of time doing mathematics you learn good practices and hence not writing such things becomes second nature, just as someone who does a lot of computer programming will know certain things are not good ways to code a particular algorithm.

My intention wasn't to address the original question directly, but rather to comment on how so many people have devoted so much time and effort to what is basically something an 8 year old would cover in school. How many showed the same interest when they were being tested on maths, when this effort wouldn't be a complete waste? I've seen someone mention 'associative and commutative'. How many people got to a stage in maths where those words appeared in their books or notes? Very few. How many came across it while Googling furiously and just parroted it? A lot more.

Why are people forming such strong opinions either about something they don't understand ( 0.9r=1 ) or which is just a poor way of writing something (this thread)? Would it not be more rational/sensible not to form such strong opinions on things which are either outside their understanding or pointless?

As I said, anyone who put that in front of me I'd ask for clarification. Besides, I haven't used the 'divided by' sign in more than a decade, I'd write such a thing as (6/2)(2+1) or 6/(2(1+2)) if I were doing it myself. Similarly things like 1/2/3 are sloppy notation and could be either 3/2 or 1/6, clarification would be asked for.

Bear in mind that if this were in someone's work then you'd have the previous line and the next line of their work, therefore you could deduce what they are referring to. This "What is this equal to?" type of questioning gives no context and provides the question 'in a vacuum'. Just as writing fractions etc in a particular way becomes good practice when you're doing lengthy calculations giving a step by step walk through is good practice even if you can do 4 lines in your head at once. I always do my writing up with the mindset that if I were hit by a bus tomorrow someone would be able to follow what I've written even if they were given nothing but what I've written (assuming they are familiar with the general area of maths in question). The expression in question doesn't fit that requirement.

If there is a particular ordering of doing things then its not followed enough that you wouldn't have to ask the person who wrote 6÷2(1+2) to clarify themselves. After all, if you're coming across this in day to day life then you're basically asking "What did the person who wrote it mean?" and then you have to wonder if they knew anything about which way to order operations. Hence asking for clarification is the only real practical way of interpreting it properly, else you send time finding out the proper way, if it exists and assuming the author knew it. In all likelihood if the author knew about such things as commutation and associativity then they'd be sufficiently practised in algebra to know not to write such things.

 

[Haircut]

Everything can be proved from first principals, so where did this "left to right convention" come from? Why does it have to be used at all? Can you find any information about it other than some primary school examples?

Let me guess "err... you're sidetracking the thread"

http://en.wikipedia.org/wiki/Operator_associativity

This is all people mean when they're referring to the "left to right convention"

 

[FoxEye]

Everything can be proved from first principals, so where did this "left to right convention" come from? Why does it have to be used at all? Can you find any information about it other than some primary school examples?

Let me guess "err... you're sidetracking the thread"

OK, while we're reinventing math, I want to define the meaning of A/B as "B divided by elephants".

Anyhow, I'm off for a drive. I think I'll drive on the right-hand side of the road today, because driving on the left is something made up by driving instructors.

Once you become an experienced driver you understand how driving on either side of the road is acceptable.

 

[Deadbeat]

http://en.wikipedia.org/wiki/Operator_associativity

This is all people mean when they're referring to the "left to right convention"

I may have been imagining it, but wasn't it this very thread that had a chuckle over using Wikipedia as a source because this exact question was edited twice within a few hours to display first one anser and then the other?

 

[gambitt]

OK, while we're reinventing math, I want to define the meaning of A/B as "B divided by elephants".

I didn't expect you to understand the meaning of "proof by first principals"

 

[dowie]

Here you go, I found it a couple of pages back; I await silence or sidetracking, your choice:

Sidetracking tbh...

There is a convention - I don't think anyone is trying to argue that the question isn't a bit silly - but I'll still argue that there is a convention for using basic operators and that in itself isn't ambiguous.

 

[gambitt]

http://en.wikipedia.org/wiki/Operator_associativity

This is all people mean when they're referring to the "left to right convention"

quote from wiki:

The associativity and precedence of an operator is a part of the definition of the programming language; different programming languages may have different associativity and precedence for the same operator symbol.

So this rule has nothing to do with the fundamental laws of mathematics but rather for sloppy programmers to avoid compiler errors

 

[silversurfer]

http://bit.ly/jfmEJh


Google says 9, computer knows all

(6 / 2) * (1 + 2) = 9
More about calculator.

 

[dowie]

Everything can be proved from first principals, so where did this "left to right convention" come from? Why does it have to be used at all? Can you find any information about it other than some primary school examples?

Let me guess "err... you're sidetracking the thread"

Explain why 2x^2 is read as 2(x^2) rather than (2x)^2 other than simply by convention.

 

[dowie]

Google says 9, computer knows all

So will excel and most modern calculators... The developers of which haven't forgotten how to use very basic operators to solve very basic problems.

 

[gambitt]

Explain why 2x^2 is read as 2(x^2) rather than (2x)^2 other than simply by convention.

Because x² = x*x so 2x² = 2*x*x not 4*x*x

 

[dowie]

Because x² = x*x so 2x² = 2*x*x not 4*x*x

you've already made an assumption of 2(x^2)

the question was

Explain why 2x^2 is read as 2(x^2) rather than (2x)^2 other than simply by convention.

Without convention this could be read as 2x * 2x or 2*x*x

You *know* that it is 2(x^2) however you only know that it is due to convention. If that convention didn't exist then you could argue that it is ambiguous as people are attempting to do within this thread.

 

[Haircut]

quote from wiki:

The associativity and precedence of an operator is a part of the definition of the programming language; different programming languages may have different associativity and precedence for the same operator symbol.

So this rule has nothing to do with the fundamental laws of mathematics but rather for sloppy programmers to avoid compiler errors

The fact remains that an operator needs to be left-associative, right-associative or non-associative.
For the example given on that page: 7 − 4 + 2 there are a few possible scenarios.
If left-associative then it's 5. Right-associative it's 1. Non-associative we would need brackets.

Another wiki link I'm afraid, but there is a convention in maths that the above operations are left-associative, so we don't need brackets and can get the answer of 5.

http://en.wikipedia.org/wiki/Associativity#Notation_for_non-associative_operations

 

[FoxEye]

I didn't expect you to understand the meaning of "proof by first principals"

You haven't proved a darn thing so far in this entire thread. You haven't even tried to do anything apart from take pot-shots at people.

Tbh it's completely pointless talking to you. You may be convinced of your own position but you have done _nothing_ to sway anyone over to your side.

And in the face of a large amount of evidence you have simply buried your head in the sand, occasionally popping up to stir things and goad someone else into wasting time on you.

Enough.